Module 1-1 Continued

1. Module 1-1 Continued Nature and Properties of Light

2. Basic Concepts Section 5 Other wave properties of light • Other important wave properties of light that deserve a brief mention in this introductory module are • Phase • Coherence • Polarization

3. Basic Concepts Section 5 • The phase of any point on a wave is defined as “the angular displacement” of that point from the last positive zero crossing of the wave. • A “positive zero crossing” occurs at those zero displacement points where the new displacement is about to become positive. • Points A and B of Figure 1-6 are positive zero crossings of the wave illustrated. At these points, the phase is zero.

4. Basic Concepts Section 5 • Figure 1.6 Sine wave representation

5. Basic Concepts Section 5 • The absolute phase of a point on a wave usually is of little interest when one is dealing with light waves, but the phase difference between two waves is often of great interest. • For example, the phase difference between points O and P on the sine wave in Figure 1-6 is 330º – 150º = 180º. • Figure 1-7 illustrates the idea of “phase difference.”

6. Basic Concepts Section 5 • Figure 1.7 Phase difference between several points • on two sine waves

7. Basic Concepts Section 5 • Wave coherence • Laser light is coherent light. Light waves are said to be “coherent” if they are all in phase with one another. • Figure 1-8 illustrates the difference between coherent light and incoherent light.

8. Basic Concepts Section 5 • The five waves shown in Figure 1-8a are coherent since each corresponding point on each wave has the same phase angle as the others, all along the length of the waves. • When added together, coherent waves, produce an overall wave of much greater amplitude—higher peaks and lower valleys.

9. Basic Concepts Section 5 • By contrast, Figure 1-8b illustrates four waves that are incoherent. • They do not possess identical phase angles along a vertical line such as YY′ and their wavelengths are all different. • When added together they generally produce an overall wave of smaller displacements with varying amplitudes along the curve. • Light can be of the same wavelength but incoherent, as well. The conditionfor being “incoherent” is that the phase angle is random.

10. Basic Concepts Section 5 • Figure 1-8(a) Coherent light. Each of the five waves has the samephase angle along the vertical line YY’, and all have the same wavelength.

11. Basic Concepts Section 5 • Figure 1-8(b) Incoherent light. Each of the four curves has a different wavelength and their phases are differentalong any vertical line YY’.

12. Basic Concepts Section 5 • As shown earlier in Figure 1-3, electromagnetic waves—and thus light waves—are made up of vibrating electric and magnetic fields. • The polarization of light refers to the orientation or directionof vibration of the electric field as the wave propagates through space.

13. Basic Concepts Section 5 • The following terms commonly are used in the description of polarized light: • Unpolarized light has no specific orientation of electric field. The direction of the electric field varies randomly at approximately the frequency of light. In Figure 1-9a, this randomness is depicted by the electric field having several different orientations.

14. Basic Concepts Section 5 • Plane-polarized light is light in which the electric field oscillates in one plane only, as in Figures 1-9b,c. • In horizontally polarized light (Figure 1-9b), the plane that contains the electric field is horizontal—perpendicular to the plane of the paper—as pictured in the head-on view. • In vertically polarized light (Figure 1-9c), the plane of the electric field is vertical—up and down in the plane of the paper and shown as vertical arrows in the head-on view.

15. Basic Concepts Section 5 • Figure 1.9 Representations of polarized light

16. Basic Concepts Section 5 • Figure 1-10 illustrates the operation of an optical element termed a “linear polarizer.” • It consists of a plastic sheet that contains needle-shaped crystals of herapathite (an iodine compound). • These crystals strongly absorb the horizontal components depicted in Figure 1-10, but they transmit most of the vertical components

17. Basic Concepts Section 5 • Figure 1.10 Polarization by absorption